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A371680 G.f. satisfies A(x) = ( 1 + x * A(x)^2 * (1 + A(x)) )^2.

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%I A371680 #8 Apr 03 2024 11:12:37
%S A371680 1,4,44,648,10960,200992,3886928,78043488,1611405504,33998715264,
%T A371680 729793915264,15886841223936,349900041893376,7782694227059712,
%U A371680 174573007616191744,3944500600180286976,89696369377912622080,2051147782339517224960
%N A371680 G.f. satisfies A(x) = ( 1 + x * A(x)^2 * (1 + A(x)) )^2.
%F A371680 G.f.: B(x)^2 where B(x) is the g.f. of A363380.
%F A371680 a(n) = Sum_{k=0..n} binomial(n,k) * binomial(4*n+2*k+2,n)/(2*n+k+1).
%o A371680 (PARI) a(n, r=2, t=4, u=2) = r*sum(k=0, n, binomial(n, k)*binomial(t*n+u*k+r, n)/(t*n+u*k+r));
%Y A371680 Cf. A363380, A371693.
%K A371680 nonn
%O A371680 0,2
%A A371680 _Seiichi Manyama_, Apr 02 2024